arXiv:2610. 29798v1 Announce Type: new Abstract: In likelihood-free hypothesis testing (LFHT), given samples from two unknown distributions $P,Q$ on $[n]$ with $\mathrm{d_{TV}}(P,Q)\geq\varepsilon$, and from a third distribution $D\in\{P,Q\}$, the goal is to identify whether $D=P$ or $D=Q$.
In likelihood-free hypothesis testing (LFHT), given samples from two unknown distributions $P,Q$ on $[n]$ with $\mathrm{d_{TV}}(P,Q)\geq\varepsilon$, and from a third distribution $D\in\{P,Q\}$, the g...
arXiv:2509. 03734v3 Announce Type: replace-cross Abstract: In the hypothesis selection problem, we are given sample and query access to finite set of candidate distributions (hypotheses), $\mathcal{H} = \{H_1, \ldots, H_n\}$, and samples from an unknown distribution $P$, both over a domain $\mathcal{X}$.
arXiv:2610. 37272v1 Announce Type: new Abstract: We study the computational limits of clustering $n$ observations drawn from a mixture of $K$ isotropic distributions in $\mathbb R^d$, in the regime where the number $K$ of groups is much larger than the dimension $d$.
arXiv:2004. 05813v3 Announce Type: replace-cross Abstract: Suppose that we are given independent, identically distributed random samples $x_1,\cdots,x_n$ from a mixture at most $k$ many $d$-dimensional spherical Gaussian distributions $\mu_1,\cdots,\mu_{k_0}$ of identical and known variance $\sigma^2$ in each coordinate, such that the minimum $\ell^2$ distance between two distinct centers $y_l$ and $y_j$ is greater than $2\Delta\sigma \min\{\sqrt{d},\sqrt k\}$, where $\Delta>C_0$, and $C_0$ is a sufficiently large universal constant.
arXiv:2409. 10908v3 Announce Type: replace-cross Abstract: Recovering the underlying $k$-clustering of a set $U$ of $n$ points by asking pair-wise same-cluster queries has garnered significant interest in the past few years.
arXiv:2608. 06262v1 Announce Type: new Abstract: Model evaluations may fix all tests before observing any responses or select later tests using earlier responses.
arXiv:2607. 15645v1 Announce Type: cross Abstract: Motivated by the challenge of testing distributions over high-dimensional or continuous domains, we study distribution testing with respect to bounded classes of distinguishers.
The paper presents tight bounds for equivalence testing using non‑adaptive conditional samples. It shows that determining whether two unknown distributions are identical or ε‑far in total variation distance requires ∫Θ((log n)/ε²) queries. Consequently, the query complexity for uniformity, identity, and equivalence testing with non‑adaptive conditional samples is ∫Θ(log n).
arXiv:2610.20375v1 Announce Type: cross Abstract: Given $n$ distributions (hypotheses) $\mathcal H=\{H_1,\ldots,H_n\}$ and samples from an unknown target distribution $P$, proper hypothesis selection...
arXiv:2608. 04288v1 Announce Type: new Abstract: Calibration requires a predictor to be unbiased after conditioning on its own predictions.
arXiv:2504. 19952v2 Announce Type: replace-cross Abstract: We present two general lower bounds for stopping times of sequential tests between arbitrary composite nulls $\mathcal P$ and alternatives $\mathcal Q$.
arXiv:2607. 24732v1 Announce Type: cross Abstract: Motivated by learning from heterogeneous and overlapping data providers, we study a stylized model of distribution learning from restricted conditional samples.